Use the definitions of sin(z) and cos(z) given in Lecture 13 at the 13:30 mark to prove that sin z+- = cos(z) for all z E C. 2 %3D (Do not use any other trigonometry identities for question 9) 1 ja-ra 10. Evaluate (3t – i)²dt 9.
Use the definitions of sin(z) and cos(z) given in Lecture 13 at the 13:30 mark to prove that sin z+- = cos(z) for all z E C. 2 %3D (Do not use any other trigonometry identities for question 9) 1 ja-ra 10. Evaluate (3t – i)²dt 9.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Question 9
Question 10
![Show that u(x, y)= 2x –x' +3xy´ is harmonic and find a harmonic conjugate
v(x, y).
Show that exp(z²) s exp(z[*) for all z e C.
5.
6.
Show that Log[(-1+i)’]# 2Log(-1+i).
7.
Find all roots of the equation log(z) = 7i / 2
8.
Find the principal value of (1+ i)'.
9.
Use the definitions of sin(z) and cos(z) given in Lecture 13 at the 13:30 mark to
prove that sin z+
= cos(z) for all z E C.
(Do not use any other trigonometry identities for question 9)
10.
Evaluate(3t - i)²dt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfc5bdab-6654-444e-b9d5-5fc4b8470fbb%2Fd8d05e54-e605-48b5-bae2-b15e7b8ce76e%2Fyfit6m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Show that u(x, y)= 2x –x' +3xy´ is harmonic and find a harmonic conjugate
v(x, y).
Show that exp(z²) s exp(z[*) for all z e C.
5.
6.
Show that Log[(-1+i)’]# 2Log(-1+i).
7.
Find all roots of the equation log(z) = 7i / 2
8.
Find the principal value of (1+ i)'.
9.
Use the definitions of sin(z) and cos(z) given in Lecture 13 at the 13:30 mark to
prove that sin z+
= cos(z) for all z E C.
(Do not use any other trigonometry identities for question 9)
10.
Evaluate(3t - i)²dt
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